Extensional rheometry of mobile fluids. Part II: Comparison between the uniaxial, planar and biaxial extensional rheology of dilute polymer solutions using numerically-optimized stagnation point microfluidic devices

In Part I of this paper [Haward et al. submitted (2023)], we presented a new three-dimensional microfluidic device (the optimized uniaxial and biaxial extensional rheometer, OUBER) for generating near-homogeneous uniaxial and biaxial elongational flows. In this Part II of the paper, we employ the OUBER device to examine the uniaxial and biaxial extensional rheology of some model dilute polymer solutions. We also compare the results with measurements made under planar extension in the optimized-shape cross-slot extensional rheometer [or OSCER, Haward et al. Phys. Rev. Lett. (2012)]. In each case (uniaxial, planar and biaxial extension), we use micro-particle image velocimetry to measure the extension rate as a function of the imposed flow rate, and we measure the excess pressure drop across each device in order to estimate the tensile stress difference generated in the fluid. We present a new analysis, based on solving the macroscopic power balance for flow through each device, to refine the estimate of the tensile stress difference obtained from the measured pressure drop. Based on this analysis, we find that for our most dilute polymer sample, which is "ultradilute", the extensional viscosity is well described by the finitely extensible non-linear elastic dumbbell model. In this limit, the biaxial extensional viscosity at high Weissenberg numbers (Wi) is half that of the uniaxial and planar extensional viscosities. At higher polymer concentrations, the experimental measurements deviate from the model predictions, which is attributed to the onset of intermolecular interactions as polymers unravel in the extensional flows. Of practical significance (and fundamental interest), elastic instability occurs at a significantly lower Wi in uniaxial extensional flow than in either biaxial or planar extensional flow, limiting the utility of this flow type for extensional viscosity measurement

Structure-property relationship of a soft colloidal glass in simple and mixed flows

HypothesisUnder specific conditions, rod-like cellulose nanocrystals (CNC) can assemble into structurally ordered soft glasses (SGs) with anisotropy that can be controlled by applying shear. However, to achieve full structural control of SGs in real industrial processes, their response to mixed shear and extensional kinematics needs to be determined. We hypothesise that by knowing the shear rheology of the CNC-based soft glass and adopting a suitable constitutive model, it is possible to predict the structure-property relationship of the SG under mixed flows.ExperimentsWe use an aqueous suspension with 2 wt% CNC at 25 mM NaCl to form a structurally ordered SG composed of a CNC network containing nematic domains. We combine rheometry and microfluidic experiments with numerical simulations to study the flow properties of the SG in shear, extension, and mixed flow conditions. Extensional flow is investigated in the Optimised Shape Cross-slot Extensional Rheometer (OSCER), where the SG is exposed to shear-free planar elongation. Mixed flow kinematics are investigated in a benchmark microfluidic cylinder device (MCD) where the SG flows past a confined cylinder in a microchannel.FindingsThe SG in the MCD displays a velocity overshoot (negative wake) and a pronounced CNC alignment downstream of the cylinder. Simulations using the thixotropic elasto-visco-plastic (TEVP) model yield near quantitative agreement of the velocity profiles in simple and mixed flows and capture the structural fingerprint of the material. Our results provide a comprehensive link between the structural behaviour of a CNC-based SG and its mechanistic properties, laying foundations for the development of functional, built-to-order soft materials

Asymmetric flows of complex fluids past confined cylinders: A comprehensive numerical study with experimental validation

Three non-Newtonian constitutive models are employed to investigate how fluid rheological properties influence the development of laterally asymmetric flows past confined cylinders. First, simulations with the shear-thinning but inelastic Carreau-Yasuda model are compared against complementary flow velocimetry experiments on a semidilute xanthan gum solution, showing that shear-thinning alone is insufficient to cause flow asymmetry. Next, simulations with an elastic but non-shear-thinning finitely extensible non-linear elastic dumbbell model are compared with experiments on a constant viscosity solution of poly(ethylene oxide) (PEO) in an aqueous glycerol mixture. The simulations and the experiments reveal the development of an extended downstream wake due to elastic stresses generated at the stagnation point but show no significant lateral asymmetries of the flow around the sides of the cylinder. Finally, the elastic and shear-thinning linear Phan-Thien-Tanner (l-PTT) model is compared with experimental velocimetry on a rheologically similar solution of PEO in water. Here, at low flow rates, lateral symmetry is retained, while the growth of a downstream elastic wake is observed, in qualitative similarity to the non-shear-thinning elastic fluids. However, above a critical flow rate, the flow bifurcates to one of the two stable and steady laterally asymmetric states. Further parameter studies with the l-PTT model are performed by varying the degrees of shear-thinning and elasticity and also modifying the confinement of the cylinder. These tests confirm the importance of the coupling between shear-thinning and elasticity for the onset of asymmetric flows and also establish stability and bifurcation diagrams delineating the stable and unstable flow states

Evaluation of constitutive models for shear-banding wormlike micellar solutions in simple and complex flows

Wormlike micellar solutions possess complex rheology: when exposed to a flow field, the wormlike micelles may orientate, stretch, and break into smaller micelles. Entangled wormlike micellar solutions exhibit shear banding characteristics: macroscopic bands with different local viscosities are organized and stacked along the velocity gradient direction, leading to a non-monotonic flow curve in simple shear. We present a systematic analysis of four commonly used constitutive models that can predict a non-monotonic flow curve and potentially describe the rheology of entangled wormlike micellar solutions with shear-banding characteristics: the Johnson–Segalman, the Giesekus, the thixotropic viscoelastic, and the Vasquez–Cook–McKinley (VCM) models. All four constitutive models contain a stress diffusion term, to account for a smooth transition between the shear bands and ensure a uniqueness of the numerical solution. Initially, the models are fitted to shear and extensional experimental data of a shear-banding wormlike micellar solution. Subsequently, they are employed to solve three non-homogeneous flows: the Poiseuille flow in a planar channel, the flow in a cross-slot geometry, and the flow past a cylinder in a straight channel. Each of these flows exposes the wormlike micellar solution to different flow kinematics (shear, extensional, and mixed), revealing different aspects of its rheological response. The predictive capability of each model is evaluated by directly comparing the numerical results to previously published experimental data obtained from microfluidic devices with corresponding flow configurations. While all the models can describe qualitatively the characteristic features observed experimentally in the benchmark flows, such as plug-like velocity profiles and elastic instabilities, none of them yields a quantitative agreement. Based on the overall performance of the models and also accounting for their differing numerical complexity, we conclude that the Giesekus model is at present the most suitable constitutive equation for simulating shear banding wormlike micellar solutions in flows that exhibit both shear and extensional deformations. However, the quantitative mismatch between model predictions and experiments with wormlike micellar solutions demand that improved constitutive models be developed in future works

Transition between solid and liquid state of yield-stress fluids under purely extensional deformations

We report experimental microfluidic measurements and theoretical modeling of elastoviscoplastic materials under steady, planar elongation. Employing a theory that allows the solid state to deform, we predict the yielding and flow dynamics of such complex materials in pure extensional flows. We find a significant deviation of the ratio of the elongational to the shear yield stress from the standard value predicted by ideal viscoplastic theory, which is attributed to the normal stresses that develop in the solid state prior to yielding. Our results show that the yield strain of the material governs the transition dynamics from the solid state to the liquid state. Finally, given the difficulties of quantifying the stress field in such materials under elongational flow conditions, we identify a simple scaling law that enables the determination of the elongational yield stress from experimentally measured velocity fields

Testosterone Therapy: An Assessment of the Clinical Consequences of Changes in Hematocrit and Blood Flow Characteristics

Baye

Shear-banded flows and elastic instabilities of wormlike micellar solutions in microfluidic devices

Non UBCUnreviewedAuthor affiliation: Okinawa Institute of Science and TechnologyPostdoctora

Δυναμική ανάλυση ελαστικών ασταθειών σε ροές σύνθετων ρευστών

Hydrodynamic instabilities are encountered during the motion of non-Newtonian fluids at low flow rates and in the absence of inertia, buoyancy, and surface tension. These unexpected flow configurations, called elastic instabilities, do not arise in the corresponding flows of Newtonian fluids at the same flow rates, and stem from the interaction of the macroscopic flow with the internal microstructure of the complex fluid. Given the plethora of materials that can be classified as complex fluids (polymer solutions and melts, crude oil, blood, foams, emulsions, lava, soft media, etc.), one can envision that such elastic instabilities play a crucial role in the evolution of a wide range of physical, biological and industrial processes. Considering the fact that such elastic instabilities arise at high values of the Weissenberg number (Wi quantifies the level of elasticity in complex fluids), and that current finite element methods cannot reach such values of Wi, because of a notoriously famous numerical instability referred to as the “High Weissenberg Number Problem” (HWNP); we developed a novel finite element formulation that circumvents the HWNP and at the same time yields an extreme reduction in the cost of transient simulations in 2 and 3 dimensions. Using this numerical formalism, we simulated flows of viscoelastic solutions, elasto-visco-plastic materials and entangled polymer melts under conditions that trigger elastic instabilities, which have been observed experimentally but have never been captured theoretically. By means of parametric analysis, we investigated in detail the impact of the rheological properties on the onset criteria of such elastic instabilities. In some cases, we accessed regions of the parameter space where inertial and capillary effects become comparable to elastic effects and studied their interplay on the flow configuration. More specifically, such techniques were employed to: 1) Correlate the presence of certain proteins in human blood plasma with in vitro observed elastic instabilities during its flow, 2) Study the effect of the rheological properties of polymer solutions on the preferential asymmetric passage of the fluid in totally symmetric geometries, 3) Derive experimental protocols for the characterization of the stress-induced transition from solid to liquid state of gels and emulsions under pure extensional deformations, and 4) Investigate the role of the rheological properties of pressure sensitive adhesives on their adhesion energy. Through our analysis, we provided a deeper understanding of the underlying physical mechanisms that cause these elastic instabilities, and aimed at the development of improved, built-to-order materials for various applications.Υδροδυναμικές αστάθειες απαντώνται κατά την κίνηση μη-Νευτώνειων ρευστών ακόμη και σε χαμηλούς ρυθμούς ροής, απουσία αδρανειακών δυνάμεων, δυνάμεων άνωσης λόγω διαφοράς πυκνότητας και δυνάμεων λόγω επιφανειακής τάσης. Αυτές οι απρόβλεπτες διαμορφώσεις της ροής ονομάζονται ελαστικές αστάθειες, δεν συμβαίνουν κατά την αντίστοιχη κίνηση Νευτώνειων ρευστών στους ίδιους ρυθμούς ροής και οφείλονται σε αλληλεπιδράσεις της εσωτερικής μικροδομής του σύνθετου ρευστού λόγω ροής. Δεδομένου του πλήθους των υλικών που μπορούν να χαρακτηριστούν ως σύνθετα ρευστά (πολυμερικά διαλύματα και τήγματα, αργό πετρέλαιο, αίμα, αφροί, αιωρήματα, λάβα, μαλακά υλικά κ.λπ.), είναι προφανές ότι τέτοιου είδους ελαστικές αστάθειες παίζουν σημαντικό ρόλο στην εξέλιξη ενός μεγάλου εύρους φυσικών, βιολογικών και βιομηχανικών διεργασιών. Λαμβάνοντας υπ’ όψη το γεγονός ότι τέτοιου είδους ελαστικές αστάθειες συμβαίνουν σε υψηλές τιμές του αριθμού Weissenberg (ο Wi ποσοτικοποιεί το βαθμό της ελαστικότητας των σύνθετων ρευστών), και ότι οι υπάρχουσες μέθοδοι πεπερασμένων στοιχείων δεν μπορούν να φτάσουν σε τόσο ψηλές τιμές του Wi λόγω μίας διαβόητης αριθμητικής αστάθειας, κοινώς γνωστής στη βιβλιογραφία ως «HighWeissenberg Number Problem» (HWNP); αναπτύξαμε μία καινοτόμο μέθοδο πεπερασμένων στοιχείων που δεν περιορίζεται από το HWNP και ταυτόχρονα προσφέρει μία τεράστια μείωση στο υπολογιστικό κόστος των χρονομεταβαλλόμενων προσομοιώσεων σε 2 και 3 διαστάσεις. Χρησιμοποιώντας αυτόν τον αριθμητικό φορμαλισμό, προσομοιώσαμε ροές ιξωδοελαστικών διαλυμάτων, ιξωδο-ελαστο-πλαστικών υλικών και διαπλεγμένων πολυμερικών τηγμάτων υπό συνθήκες που εμφανίζουν ελαστικές αστάθειες, οι οποίες έχουν παρατηρηθεί πειραματικά, αλλά δεν έχουν προσομοιωθεί ποτέ. Πραγματοποιώντας εκτενείς παραμετρικές αναλύσεις, εξετάσαμε εις βάθος το ρόλο των ρεολογικών ιδιοτήτων στα κριτήρια εμφάνισης τέτοιων ελαστικών ασταθειών. Σε κάποιες περιπτώσεις, εξερευνήσαμε περιοχές του παραμετρικού χώρου όπου οι αδρανειακές και τριχοειδείς δυνάμεις γίνονται συγκρίσιμες με τις ελαστικές δυνάμεις και μελετήσαμε την αλληλεπίδρασή τους στη διαμόρφωση των ροϊκών πεδίων. Πιο συγκεκριμένα, τέτοιου είδους τεχνικές χρησιμοποιήθηκαν για: 1) Τη συσχέτιση της παρουσίας ορισμένων πρωτεϊνών στο πλάσμα του ανθρώπινου αίματος με ελαστικές αστάθειες που έχουν παρατηρηθεί κατά τη ροή του, 2) Τη μελέτη του ρόλου των ρεολογικών ιδιοτήτων πολυμερικών διαλυμάτων στο φαινόμενο κατά το οποίο το ρευστό προτιμάει τη διέλευση μέσω συγκεκριμένων μονοπατιών διαμορφώνοντας ασύμμετρα ροϊκά πεδία σε απόλυτα συμμετρικές γεωμετρίες, 3) Τη θεμελίωση πειραματικών πρωτοκόλλων για το χαρακτηρισμό ιξωδο-ελαστο-πλαστικών υλικών και ειδικά της μετάβασης τους από τη στερεή στη ρευστή κατάσταση υπό την επήρεια μόνο εκτατικών παραμορφώσεων και 4) Τη συσχέτιση των ρεολογικών ιδιοτήτων των πιεζοευαίσθητων συγκολλητικών με την συγκολλητική τους ενέργεια. Μέσα από την παρούσα ανάλυση, προσφέρεται μία βαθιά κατανόηση των φυσικών φαινομένων που προκαλούν αυτές τις ελαστικές αστάθειες, αποσκοπώντας στην ανάπτυξη βελτιωμένων υλικών με προδιαγεγραμμένες ιδιότητες που προορίζονται για διάφορες εφαρμογές